CHAPTER 19
Causation
19.1 The Nature of Causation
It was the 18th-century philosopher David Hume who fIrst drew attention to the fact that no one has ever directly observed a causal connection,
or as he described it 'a necessary connection', between two events. Experience tells us that certain events are usually immediately followed by
certain others, and the experience sets up in us an anticipation of such consequences. To say that one event 'causes' another, however, is not to
offer an explanation; it is simply a handy way of describing our observations. Why does one magnet attract another? We can offer descriptions at
atomic and even sub-atomic levels, and we can model the attraction in mathematical terms so that we can predict the behaviour of magnets with
very great accuracy, but we are still faced with a basic lack of planation as to why one magnetic pole attracts another of opposite polarity.
Indeed the very ideas of 'attraction' and 'magnetic pole' are human inventions created to organise our thoughts about these phenomena.
Psychological experiments have shown that people have a tendency to assume a causal connection between any two relatively rare events
if one happens immediately before the other. If the juxtaposition of such events is repeated the impression of causal connection is strengthened.
Just as we are disposed to see our world in terms of 'entities' rather than in terms of a confused collection of patches of colour, so we tend to
perceive a chronological sequence of isolated events as a single extended event. Causation is perceptual 'glue' which combines
several events to form one. It is a product of the human mind which renders predictable that which is otherwise unpredictable.
19.2 Notation
Let us represent the causal connection between any two events X and Y by the notation 'X --> Y'.
Sometimes it is helpful to provide a graphical representation of causal connections.
When it is appropriate we shall use the notation illustrated in Figure 19.1.
19.3 The Transitivity of Causal Connections
Causation is transitive. That is, if we observe that (X causes Y) and (Y causes Z), we can infer that (X causes Z), or in the new notation:
(X --> Y) and (Y --> Z) =>> (X --> Z)
or more succinctly:
(X --> Y --> Z) ==> (X --> Z)
where ==>> means 'implies'.
Furthermore we can, if the situation warrants it, insert extra events between A and Z to give:
(A --> B --> C --> D --> ......... Z)
We have been using the term 'event' rather loosely so far. If we return to the ideas introduced in section 4.3, where we discussed object-histories
of objects in the micro-graphics world, we can represent our view of the world as a chronological sequence of 'states'.
A state is a condition of the world perceived at some particular time or over a particular period of time.
The expression (A --> B --> C --> D ... Z) should then be interpreted as a sequence of causally linked states (rather than events).
A causal connection exists between states if we find that we can use the observation of one state to predict (with reasonable confidence)
the future observation of the other.
19.4 Causal Links and Time-stamps
When we speak about causation, we are sometimes discussing a general rule which applies to all occasions.
For example 'Disease causes death'. On other occasions we are speaking of a particular set of circumstances,
e.g. 'The King's death was caused by Bubonic Plague'.
The second case is the more interesting because the states concerned, which represent the King alive (A), and the King dead (Z),
have, presumably, actually been observed and will have particular time-stamps. We are saying that (in our opinion) certain
other states intervened between A and Z to form a causally linked chain of states (A, B, C, ... Z) where B, C, etc. are states
describing the King catching Bubonic Plague, developing a temperature, and so on. We are saying that each state in the
chain was directly responsible for the next, and that these causal links (or connections) actually happened at particular
moments in time. Something which happened at a particular moment in time can be represented as;
a state (since it represents a perceived condition of the world). It follows that a causal connection can be
represented by a 'state'.
This is an important conclusion because it means that a causal connection can itself be the causal precursor or the
consequence of some other state. In other words a 'cause' can cause a 'cause'. To implement our representation we
can use a predicate 'cause(X, Y)', or a data structure of type 'cause' with elements holding pointers to X and Y.
It does not matter which. What we cannot do, however, is
to provide a representation of X with a simple pointer (labelled 'cause') to Y (or vice versa). The representation of the
causal link between X and Y must be independent of the representations X and Y so that it can have its own identity
and its own time-stamp.
A causal connection of the type 'Disease causes death' is timeless (has a formal parameter as its time-stamp) and
is analogous to the generic structures we introduced to deal with concepts. It can be used to generate an infinite set
of particular examples of causal links.
When we say 'X caused Y' it could be the case that X has been observed and Y is being inferred.
It could also be the case that Y has been observed and X is being inferred (as in forensic science).
It is also possible that both X and Y have been observed and we are asserting that it is our perception that there was a
causal link between them. The interpretation of this last type is interesting because it introduces the idea of
hypothetical situations. We are in fact asserting that if X had not occurred, Y would not have occurred (at the time that it did occur).
The implication is that we must be able to represent hypothetical states.
19.5 Types of Causal Link
There appear to be several different types of causal connection, but because a 'cause' can cause a 'cause' a single type of representation of causal linkage can be used for all of those types.
Multiple causes
Gating. This is really a disguised form of the multiple cause condition, where most oUhe multiple causes are
normally present and one remaining condition (state) is caused by X. We can reduce the complexity of the
representation, however, as illustrated in fig 19.3.
Negative gating. For this form of representation we need to be able to negate states.
19.6 Ignoring Causal Links
In many cases causal links are implicit in the use of certain words, and the speaker is concerned to
add additional information which extends the causal chain, or inserts additional links into it.J\n example
we have already used is 'He drowned because he fell into the water'.
Actually people drown because they are in water. Falling in is not by itself a cause of drowning. However,
the speaker would assume that this simple fact is known to the hearer, and is providing additional information
which indicates how the person got into the water. That is, when we use the word 'drowned' we
expect other people to interpret it in more or less the same way as we do. The meaning of the word 'drown' can
be paraphrased by the representation in Figure 19.5 corresponding to states (s3, s4, s5). If we believe that the speaker
understands our words then we must assume that he or she has the representation of s3, s4, s5. The additional information
corresponds to states sl and s2, and therefore if asked 'Why did he drown?' we supply sl, s2 as the answer.
This goes some way towards resolving the problem noted in our discussion of Conceptual Dependency Theory (section 14.9).
19.7 Summary
We have developed arguments which support the following conclusions:
(1) Causation is a product of human perception.
(2) Causation is transitive.
(3) Our representation should allow causal chains to be extended and additional links to be inserted.
(4) We require the representation of negated states.
(5) We require the representation of hypothetical states.
(6) We require the representation of other people's internal representations.
(7) A causal link can be represented as a state with its own time-stamp.
(8) A cause can cause a cause.